Klostermann starred for Germany in the European Under-21 Championship this summer and is now on the radar of a number of clubs.
Spanish publication Diario AS report that Atletico and Arsenal both want to add the 23-year-old to their squads ahead of the new season.
Lukas Klostermann starred in European Under-21 Championship for Germany this summer
For Atletico, the right-back would provide a suitable replacement for Juanfran, who left the club this summer.
Klostermann has already made two appearances for Germany at senior level and that is what has impressed Arsenal.
Klostermann has been a key player for RB Leipzig and they are not interested in selling him.
Klostermann has become a key player for RB Leipzig and they will be unwilling to sell him